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 Jun 7, 2011           

 On Hume and the problem of induction

There is a peculiarly painful chamber inhabited solely by philosophers who have refuted Hume. These philosophers, though in Hell, have not learned wisdom. They continue to be governed by their animal propensity towards induction. But every time that they have made an induction, the next instance falsifies it. This, however, happens only during the first hundred years of their damnation. After that, they learn to expect that an induction will be falsified, and therefore it is not falsified until another century of logical torment has altered their expectation. Throughout all eternity surprise continues, but each time at a higher logical level."
   -- Bertrand Russell, "The Metaphysician's Nightmare"


      1. Introduction
       2. On the induction text that follows

1. Introduction

And now for something completely different from ME/CFS - on which there is a note at the end, in my P.S. - namely text by myself on the problem of induction, in what to Bertrand Russell at one time appeared to be a bid for hell, though he himself also made a similar bid, namely in his "Human Knowledge - Its Scope and Limits".

The following is a copy of my notes to Chapter IV of Hume's "Enquiry concerning Human Understanding", and as I say at the end, it is mainly drawn from a paper I wrote in 1981, that I did not publish, but did lecture on in 1988 - after which I have been too ill to write substantially more on the topic (on which I have very extensive notes).

It's original with me and one reason to put it here is that it was recently visited quite a number of times, possibly also because of the first note, that is also original with me.

Incidentally, the reason to write "original with me" is that I thought of it myself, but would not be amazed if it has since been pinched without attribution, as rather a lot seems to have been that's on this site, indeed quite in line with the human average, that tends to have no moral norms of their own, except within the group they function, because there they will be punished for transgressions, but not elsewhere, usually.

Anyway... here is the background for what follows and the explanation of its format:

I like html - hypertext marked language - and very probably wrote the first hypertext editor for it in Holland, in Prolog, in 1990-91, called Edith, and for DOS.

My main reason to like it is that it enables new ways to deal with texts, as everybody who uses internet meanwhile must have realized, for since then Tim Berner-Lee invented a better way to do hypertext, and it is still the main format for text and contained data on the internet.

Again, my main reason to like it in a philosophical context that it seemed and seems to me to provide an excellent way for a philosopher to write extensive comments on classical (and other) philosophical texts, namely by reproducing the original and inserting hypertext links.

This is what I did in my philosophy section, with quite a few classical texts of philosophy, and several that I like a lot and consider philosophical, for the most part, although they are not traditionally reckoned to be such (see e.g. Burkhardt, Chamfort, Multatuli and Swift).

Most academic philosophers don't do this, although I think they should if they want to honestly explain what they think and why they do so, both to themselves and to others. The main reason for that is probably that doing so would take considerable effort while it would not be publishable in a modern philosophical journal, which is still - alas - the standard medium for founding an academic philosopher's career.

2. On the induction text that follows

As I said, the text that follows consists of my notes to David Hume's Section IV of his Enquiry concerning Human Understanding. It's almost wholly unchanged, and the format is that the blue text is Hume's and the black text my comments.

If there are differences with the original notes it is in the links, and if you want to consult these, or if a link in the present text fails - that has been composed with difficulties in that respect, and with failing health, in part because of ME/CFS, in part because of its severity combined with lack of any help for chronically ill since 1988 - you are adviced to turn to the original notes, where the links should work.

Finally, to my knowledge the solution I offer is new, though important parts were also seen by Charles Sanders Peirce and Bertrand Russell, and indeed by Isaac Newton, as explained in the text that follows, that should be mostly understandable by intelligent readers, since I made no attempts at false philosophical profundity, while I did try to write as clearly as I could - and indeed the problem I treat is quite fundamental and important for human knowledge, and should also be clear to anyone with a clear mind.

Notes to Section IV: Sceptical doubts concerning the operations of the understanding

Note 1: All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic; and in short, every affirmation which is either intuitively or demonstratively certain.

This is one of Hume's principles, that incidentally reminds one of a similar distinction by Leibniz between truths of fact and truths of reason. In either case, the distinction seems to me to be incomplete, and to miss something quite important, that may be referred to in Humean terms as Relations of Ideas and Facts, or in modern terms: Semantical Relations.

As the terms chosen indicate, the best and easiest examples of such relations are those that obtain between the terms of a natural language and the natural things they stand for, whatever they may be.

Also, it is clear that these relations must be learned, and have been learned to a considerable extent by anyone who knows a natural language, and indeed have been learned on the basis of associations of the sounds of speech and the facts of experience.

Furthermore, it is clear that these semantical relations relate ideas and facts with the help of the sounds of speech, and that it would be more confusing than helpful to try to reduce these Semantical Relations to either Relations of Ideas or Matters of Fact, precisely because they connect the two, and must be learned, and involve natural language, and are characteristic for human beings, since other animals may as well be claimed to have some Relations of Ideas and to know some Matters of Fact, but evidently lack the ideas required for language that would allow them to tie the two together by speech, and use that to communicate the ideas that have thus been associated to the sounds of speech.

Indeed, it is a curious fact that Hume missed this third kind of fundamental relation, and also that I have not read others who made the same point after him, though it struck me when I first read the Treatise and the Enquiries.

And it is at least fairly obvious that there are in fact three kinds of reports:

- on reality
- on experience
- on symbolizations

These three kinds of reports obviously exist, and there are considerable and systematic differences between them. Reports of real things concern what is there regardless of experience, and this may and often does differ a lot from  reports of experiences of things. And these in turn tend to be rather different from symbolizations in the wide sense of stories, drawings, etc. which involve interpretations of the symbols.

Finally, it should be mentioned here that arguments that involve what is called 'Hume's Fork' are such as to presume that human reason only involves two kinds of fundamental entities 'to wit, Relations of Ideas, and Matters of Fact', and may well be mistaken in missing the Semantical Relations, which are typically human (if indeed not Humean).

Note 2: Matters of fact, which are the second objects of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality. That the sun will not rise to-morrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise. We should in vain, therefore, attempt to demonstrate its falsehood. Were it demonstratively false, it would imply a contradiction, and could never be distinctly conceived by the mind.

This seems mostly so, and to be a relevant distinction, but it is unclear in at least three respects.

First, although Hume uses the term 'Matters of fact' what he often though not always seems to mean are sensations, that inform us about facts, but that do not coincide with them.

Second, and related to the first point, there is the fact that some sensations - such as an oar dipped in the water that appears bend while it is straight - are known to be illusive.

Third, and related to both foregoing points, there are some facts, notably geometrical diagrams, that may seem necessary in some sense. Thus, a Euclidean triangle has angles that sum to 180 degrees.

Of these points, the last two are of relatively minor importance, and possibly in the nature of nit-picking, but the first confusion, that of Matters of Fact and Sensations, is of some importance to Hume's arguments.

Note 3: It may, therefore, be a subject worthy of curiosity, to enquire what is the nature of that evidence which assures us of any real existence and matter of fact, beyond the present testimony of our senses, or the records of our memory. This part of philosophy, it is observable, has been little cultivated, either by the ancients or moderns; and therefore our doubts and errors, in the prosecution of so important an enquiry, may be the more excusable; while we march through such difficult paths without any guide or direction.

Here Hume has started to prepare the reader for his new ideas concerning Cause and Effect, in which he knew himself to be an innovator. I will turn to this in further notes, but want to record here a general answer to his implied question what it is that 'assures us of any real existence and matter of fact, beyond the present testimony of our senses'.

The answer is in two words: Experiment and assumption. That is: We know matters of fact, apart from teaching and reports, by our senses; we secure such testimony of our senses by experiments; and if we are convinced that our senses have not deceived us we may make an assumption to that effect, and assert a certain kind of - presumptive - fact, such as that birds lay eggs or that copper conducts electricity.

Now one may well ask what would justify such an assumption, and in fact there was in Hume's time a clear answer to that question, namely by Newton, who had added to the 1714-edition of his Principia a set of Rules of Reasoning.

Newton's Rules of Reasoning minus his comments (to some of which I will return) are the following, where it should be realised that in the following quotation Newton meant by "experimental philosophy" what we call "natural science" and that a shorter version of "which admit neither intensification nor remission of degrees" is "which are invariant".

Rule I : We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.
Rule II : Therefore to the same natural effects we must, as far as possible, assign the same reasons.
Rule III : The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.
Rule IV : In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may be either made more accurate, or liable to exception.

There is a complete version of Newton's Rules of Reasoning in Philosophy, including Newton's explanations, on my site.

Hence, when Hume writes 'This part of philosophy, it is observable, has been little cultivated, either by the ancients or moderns' he sounds somewhat disingenuous, especially since he does not even mention Newton here. (He does refer to these Rules in a footnote in the Enquiry concerning the Principles of Morals, though.)

However, when Hume writes, with my added stress 'It may, therefore, be a subject worthy of curiosity, to enquire what is the nature of that evidence which assures us of any real existence and matter of fact, beyond the present testimony of our senses, or the records of our memory' he asks a question that makes sense, and that I shall try to answer below.

For the moment I observe that Newton's Rules III and IV do clearly assert that 'In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined' and that 'The qualities of bodies [which are invariant - M] (..) and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever' and that it is rather inconceivable to me that Hume did not know these "Rules of Reasoning in Philosophy".

Note 4: All reasonings concerning matter of fact seem to be founded on the relation of Cause and Effect. By means of that relation alone we can go beyond the evidence of our memory and senses. If you were to ask a man, why he believes any matter of fact, which is absent; for instance, that his friend is in the country, or in France; he would give you a reason; and this reason would be some other fact; as a letter received from him, or the knowledge of his former resolutions and promises. A man finding a watch or any other machine in a desert island, would conclude that there had once been men in that island. All our reasonings concerning fact are of the same nature.

Hume is going to be quite skeptical about this 'relation of Cause and Effect', and therefore it is well to stress that he wrote that 'All reasonings concerning matter of fact seem to be founded' on it.

Also, it makes sense to remark here that Hume is quite correct in the examples he provides, but that he does not mention that in natural language the terms 'cause' and 'effect' are often used as 'reason' or 'premise' and as  'consequence' or 'conclusion', and are often used in the sense that what is termed the cause is a sufficient reason to infer in conclusion what is termed the effect.

Note 5: If we anatomize all the other reasonings of this nature, we shall find that they are founded on the relation of cause and effect, and that this relation is either near or remote, direct or collateral. Heat and light are collateral effects of fire, and the one effect may justly be inferred from the other.

This is so only with the proviso indicated in the previous note, namely that in our reasonings about nature what we use as reasons or premisses are often called causes, and what we use as conclusions from these reasons or premisses are often called effects.

Hume is right that often by the use of the phrases 'cause and effect' more is suggested than would be meant had the words 'premise and conclusion' been used, but it is not the case that this is always so, and indeed the Ancients already were aware that there are such things as probable causes, i.e. events that more likely than not have a certain effect, but not invariably so. An obvious example is "In summer it is warm in the daytime, usually".

Note 6: If we would satisfy ourselves, therefore, concerning the nature of that evidence, which assures us of matters of fact, we must enquire how we arrive at the knowledge of cause and effect.

This surely is a valid inquiry, but it should be pointed out, as I did in previous notes, that 'we arrive at the knowledge of cause and effect' often by calling our hypotheses causes, and our deductions from our hypotheses effects.  

Note 7: I shall venture to affirm, as a general proposition, which admits of no exception, that the knowledge of this relation is not, in any instance, attained by reasonings a priori; but arises entirely from experience, when we find that any particular objects are constantly conjoined with each other. Let an object be presented to a man of ever so strong natural reason and abilities; if that object be entirely new to him, he will not be able, by the most accurate examination of its sensible qualities, to discover any of its causes or effects. Adam, though his rational faculties be supposed, at the very first, entirely perfect, could not have inferred from the fluidity and transparency of water that it would suffocate him, or from the light and warmth of fire that it would consume him. No object ever discovers, by the qualities which appear to the senses, either the causes which produced it, or the effects which will arise from it; nor can our reason, unassisted by experience, ever draw any inference concerning real existence and matter of fact.

Kant, who was 'awoken from his slumbers' by reading Hume's Enquiries in reaction did 'venture to affirm' that there is an 'a priori' idea of the notion of cause and effect.

I want to avoid considering Kant, whose reasonings I find generally at least as obscure as his prose, but should, I think, remind the reader of Kant's reaction, and the fact that since Hume seems to have denied the existence of innate ideas, this attempted solution was not open for him. (But see Notes 12 and 14 to Section II)

In any case, whatever notions one is born with, Hume's examples in the quotation are adequate, and we may conclude that whether or not we have an innate tendency to reason in terms of causes and effects, the actual discovery of such a presumed relation between a particular cause and its  particular effect must be made in experience.

Incidentally, and without thinking it necessary to explain Hume's English, by the phrase 'No object ever discovers' he meant 'No object ever clearly shows'.

Note 8: This proposition, that causes and effects are discoverable, not by reason but by experience, will readily be admitted with regard to such objects, as we remember to have once been altogether unknown to us; since we must be conscious of the utter inability, which we then lay under, of foretelling what would arise from them.

This I accept, given the provisos I have made in earlier notes, and with a proviso in the next one:

Note 9: Such events, as bear little analogy to the common course of nature, are also readily confessed to be known only by experience; nor does any man imagine that the explosion of gunpowder, or the attraction of a loadstone, could ever be discovered by arguments a priori. In like manner, when an effect is supposed to depend upon an intricate machinery or secret structure of parts, we make no difficulty in attributing all our knowledge of it to experience.

I once again refer to my Notes 12 and 14 to Section II and ask, in Hume's own terms used there "what can be meant by asserting, that (..) the passion between the sexes is not innate?". Indeed, the modern answer is that this is caused by hormones acting on capacities one is born with. But I agree with Hume that even so each young man and young woman will have to discover this for himself and herself.

Note 10: We are apt to imagine that we could discover these effects by the mere operation of our reason, without experience. We fancy, that were we brought on a sudden into this world, we could at first have inferred that one Billiard-ball would communicate motion to another upon impulse; and that we needed not to have waited for the event, in order to pronounce with certainty concerning it. Such is the influence of custom, that, where it is strongest, it not only covers our natural ignorance, but even conceals itself, and seems not to take place, merely because it is found in the highest degree.

This I select because I agree with it and because I want to stress Hume's appeal to 'the influence of custom'.

Note 11: But to convince us that all the laws of nature, and all the operations of bodies without exception, are known only by experience, the following reflections may, perhaps, suffice. Were any object presented to us, and were we required to pronounce concerning the effect, which will result from it, without consulting past observation; after what manner, I beseech you, must the mind proceed in this operation? It must invent or imagine some event, which it ascribes to the object as its effect; and it is plain that this invention must be entirely arbitrary.

Here one can agree mostly with Hume without doing so fully, because it is quite possible and conceivable that such 'invention' need not 'be entirely arbitrary'. An example is the discovery of most young men in their puberty that young women are specially attractive.

But in general terms, as with the supposedly innate human 'grammar' that enables small children to rapidly learn the grammar of any natural language: What is innate, if anything, is in all likelihood quite general and abstract, and needs combination with specific experiences to be developed.

Note 12: May not both these balls remain at absolute rest? May not the first ball return in a straight line, or leap off from the second in any line or direction? All these suppositions are consistent and conceivable. Why then should we give the preference to one, which is no more consistent or conceivable than the rest? All our reasonings a priori will never be able to show us any foundation for this preference.

Again a caveat must be introduced: In so far as what we explain is explained by mathematics, some hypotheses we might make may seem more sensible than others, not because of what we know about the natural facts we attempt to explain, but because the mathematical formulas are clearer, simpler or more beautiful than they would be for other hypotheses we could conceive.

Precisely what weight should be given to this consideration is difficult to say, but it is a fact that quite a few prominent physicists have revealed that part of their motivations to select a certain hypothesis, that later was confirmed experimentally, was the mathematical beauty of the formulas necessary to state the hypothesis.

Note 13: In a word, then, every effect is a distinct event from its cause. It could not, therefore, be discovered in the cause, and the first invention or conception of it, a priori, must be entirely arbitrary. And even after it is suggested, the conjunction of it with the cause must appear equally arbitrary; since there are always many other effects, which, to reason, must seem fully as consistent and natural. In vain, therefore, should we pretend to determine any single event, or infer any cause or effect, without the assistance of observation and experience.

This is again a conclusion I agree to, apart from a few provisos made in previous notes.

Also, it should be remarked that Hume's general mode of reasoning is much unlike that of the Scholastics, who tended to presume that all manner of things concerning the world, human beings and God, could be derived by a priori reasoning. (The Summas of Aquinas are good examples of this Scholastic mode of reasoning.)

Note 14: Hence we may discover the reason why no philosopher, who is rational and modest, has ever pretended to assign the ultimate cause of any natural operation, or to show distinctly the action of that power, which produces any single effect in the universe. It is confessed, that the utmost effort of human reason is to reduce the principles, productive of natural phenomena, to a greater simplicity, and to resolve the many particular effects into a few general causes, by means of reasonings from analogy, experience, and observation. But as to the causes of these general causes, we should in vain attempt their discovery; nor shall we ever be able to satisfy ourselves, by any particular explication of them.

Obviously, this makes most philosophers before Hume appear to be not so very 'rational and modest', and evidently Hume's reasoning about 'the causes of these general causes' of which 'we should in vain attempt their discovery' applies especially to the hypothesis of divinities, angels, devils, supernatural forces etc.

Note 15: These ultimate springs and principles are totally shut up from human curiosity and enquiry. Elasticity, gravity, cohesion of parts, communication of motion by impulse; these are probably the ultimate causes and principles which we shall ever discover in nature; and we may esteem ourselves sufficiently happy, if, by accurate enquiry and reasoning, we can trace up the particular phenomena to, or near to, these general principles.

See my previous note: Hume did not believe in the divine hypothesis, and indeed held that it was both irrational and immodest to pretend to have knowledge of a God or of God's wishes, and I entirely agree:

It seems far to much like explaining what goes on in one's home by assuming that there is an extra floor in one's house that no one can see or discover, that supposedly includes a puppeteer or director who generates and controls all or most of what happens in one's house. Indeed, if your neighbour adopts such a hypothesis about his house, you will very probably regard him as mad (if not fraudulent, since so many professions of faith turn out to be profitable) and possibly dangerous, and I myself see little reason to believe otherwise about the divine hypothesis, except that I grant that some very intelligent men have also believed it, though very probably for emotional and not for rational reasons, and because, unlike me, they were raised in a religious faith.

Note 16: The most perfect philosophy of the natural kind only staves off our ignorance a little longer: as perhaps the most perfect philosophy of the moral or metaphysical kind serves only to discover larger portions of it. Thus the observation of human blindness and weakness is the result of all philosophy, and meets us at every turn, in spite of our endeavours to elude or avoid it.

Here Hume again states part of the reason for his academical scepticism, and he is certainly right, apart from the merits of academical scepticism, that it is always wise to presume that there is very much that any particular man and all men together do not know, and that there may be much that is too complex for human beings to know, or to know more than in outline, and approximately or schematically at best. 

Note 17: Nor is geometry, when taken into the assistance of natural philosophy, ever able to remedy this defect, or lead us into the knowledge of ultimate causes, by all that accuracy of reasoning for which it is so justly celebrated. Every part of mixed mathematics proceeds upon the supposition that certain laws are established by nature in her operations; and abstract reasonings are employed, either to assist experience in the discovery of these laws, or to determine their influence in particular instances, where it depends upon any precise degree of distance and quantity.

This is mostly so, but there is the point I made in Note 12, that part of the inspiration that led to natural discoveries was the mathematical beauty or simplicity of formulas. However, it may be conceded that this shows far less about nature than about the human mind, and that it is heuristic rather than factual. (Also, one is less likely to hear about mathematical theories based on beautiful formulas if these failed to be true.)

Note 18: But we have not yet attained any tolerable satisfaction with regard to the question first proposed. Each solution still gives rise to a new question as difficult as the foregoing, and leads us on to farther enquiries. When it is asked, What is the nature of all our reasonings concerning matter of fact? the proper answer seems to be, that they are founded on the relation of cause and effect. When again it is asked, What is the foundation of all our reasonings and conclusions concerning that relation? it may be replied in one word, Experience. But if we still carry on our sifting humour, and ask, What is the foundation of all conclusions from experience? this implies a new question, which may be of more difficult solution and explication.

The answer to that last question seems to along these lines: Presumption, hypothesis, or assumption - and if one asks once more what are the foundations of these, the answer seems to be: Imagination, fantasy, creativity or feelings of beauty - and the fact that one's hypotheses deductively imply conclusions one should like to explain by these hypotheses, and deductively imply nothing that is known to be false, and are consistent with one's further assumptions, and may have some empirical support that they may be true. (See below, under abduction.)

And indeed these are the only means human beings have to generate and support guesses - except, of course, that it is very wise to check such guesses as one feels one should make by experiment, and to control them by logic, and in the light of all other knowledge one supposes oneself to have.

Note 19: I shall content myself, in this section, with an easy task, and shall pretend only to give a negative answer to the question here proposed. I say then, that, even after we have experience of the operations of cause and effect, our conclusions from that experience are not founded on reasoning, or any process of the understanding. This answer we must endeavour both to explain and to defend.

It seems Hume is a little ironical here, for what follows was quite radical and new, namely a series of arguments to the effect that 'even after we have experience of the operations of cause and effect, our conclusions from that experience are not founded on reasoning, or any process of the understanding'.

These arguments I shall mostly excerpt and annotate in the text that follows, but it may be helpful to the reader to have links to my notes 4 and 5 in this text, that comment on some of the vagueries of the use and meaning of the terms "cause" and effect", and to remind the reader that Hume himself in the previous section III introduced 'Cause or Effect' as one of 'three principles of connexion among ideas'.

Note 20: It must certainly be allowed, that nature has kept us at a great distance from all her secrets, and has afforded us only the knowledge of a few superficial qualities of objects; while she conceals from us those powers and principles on which the influence of those objects entirely depends.

No doubt this is true in most relevant senses, though there are two relevant qualifications.

First, and in spite of the 'great distance' that 'nature has kept' between human beings and all of nature's 'secrets', it should be noted that there have been many discoveries of natural things and processes since the time in which Hume lived that are quite amazing and that are true at least to the extent - which is an extent that does not at all hold for religious or political ideas and ideals, that people kill and are killed for - that enormous amounts of working technology of many kinds have been based upon these discoveries of science.

Second, while nature may be presumed to keep other animals at least as far from nature's secrets as mankind, and while other animals seem rarely or never to make natural discoveries, even so they live, presumably with little acquired knowledge, and mostly based on instinct, apparently tuned to nature in ways men cannot achieve.

Note 21: But notwithstanding this ignorance of natural powers[H1] and principles, we always presume, when we see like sensible qualities, that they have like secret powers, and expect that effects, similar to those which we have experienced, will follow from them. If a body of like colour and consistence with that bread, which we have formerly eat, be presented to us, we make no scruple of repeating the experiment, and foresee, with certainty, like nourishment and support. Now this is a process of the mind or thought, of which I would willingly know the foundation.

A - classical - answer one might give here is: That like follows from like. As we shall find below, Hume is not satisfied with it.

And it may be well to outline schematically the sort of inference Hume had in mind and found problematical:

Given in experience : if a is P, then a is Q, and
                             if b is P, then b is Q, and
                             if m is P, then m is Q

one concludes

Therefore:               For every x, if x is P, then x is Q

or one concludes

Therefore:               For the next n, if n is P, then n is Q

based on the examples a .. m one found in experience. The 'like follows from like' in the present case is based on the presumed facts that a if P is also Q, b if P is also Q and so on. 

It should be obvious that Hume is right that neither inference is logically implied by the evidence, in a deductively valid manner, though the evidence  does support it to some extent.

Note 22: It is allowed on all hands that there is no known connexion between the sensible qualities and the secret powers; and consequently, that the mind is not led to form such a conclusion concerning their constant and regular conjunction, by anything which it knows of their nature. As to past Experience, it can be allowed to give direct and certain information of those precise objects only, and that precise period of time, which fell under its cognizance: but why this experience should be extended to future times, and to other objects, which for aught we know, may be only in appearance similar; this is the main question on which I would insist.

Here we have a precisification of the 'process of the mind or thought' that Hume inquired after in the previously quoted passage. The logical problem that lies behind Hume's question he himself expresses here as 'why this experience should be extended to future times, and to other objects'.

That is: What is the foundation of the judgment that like does follow from like, if we also know that this connection is not deductively valid (contingent connections need not remain as they are) nor necessary (the bread we see and believe to be nutrious in fact may be rotten)?

Note 23: The bread, which I formerly eat, nourished me; that is, a body of such sensible qualities was, at that time, endued with such secret powers: but does it follow, that other bread must also nourish me at another time, and that like sensible qualities must always be attended with like secret powers? The consequence seems nowise necessary. At least, it must be acknowledged that there is here a consequence drawn by the mind; that there is a certain step taken; a process of thought, and an inference, which wants to be explained.

Again I answer that the psychological explanation seems easy to me: We expect that like follows like, and therefore expect that what seems to be bread that looks much like the bread that nourished us before, will do so again, and indeed expect a connection to happen again the more confidently the more often we have experienced the connection.

Note 24: These two propositions are far from being the same, I have found that such an object has always been attended with such an effect, and I foresee, that other objects, which are, in appearance, similar, will be attended with similar effects. I shall allow, if you please, that the one proposition may justly be inferred from the other: I know, in fact, that it always is inferred. But if you insist that the inference is made by a chain of reasoning, I desire you to produce that reasoning. The connexion between these propositions is not intuitive. There is required a medium, which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument. What that medium is, I must confess, passes my comprehension; and it is incumbent on those to produce it, who assert that it really exists, and is the origin of all our conclusions concerning matter of fact.

I grant that Hume is quite right in the opening sentence of this quotation, and that indeed the inference from a series of similar connections of things - A1 with B1, A2 with B2, A3 with B3 and so on up to An and Bn - in the past to the statement that it will happen again, and that "therefore" An+1 will and must be joined with Bn+1 is not deductively valid.

However... an answer to Hume's 'if you insist that the inference is made by a chain of reasoning, I desire you to produce that reasoning' seems fairly simple, and is as follows, in principle, and without mathematical detail:

It would seem that the connection is not necessary but probabilistic, and that one can suppose that the mind keeps track of stable associations in a probabilistic manner, in such a way that the more often an association has been experienced without fail, the stronger the mind expects that it will happen again.

This may turn out to be a mistake, but it is not difficult - in this day and age - to write a computer program that does this, at least for specific kinds of connections. And indeed, since Hume lived, there has been an enormous development of probability-theory and statistics, including topics like correlations.

There is more on this in a later note in this section, for Hume does also briefly consider probability, and we shall then see that his objection to it is in fact the same: From the fact that something has happened 19 times out of 20 in our experience, it does not follow with logical necessity that it will continue to happen in the future in the same proportion (or indeed in any other proportion).

This is a cogent objection I shall below return to. Even so, I think I have answered part of his demand, for I have indicated what sort of reasoning might be used by the mind (or indeed a computer that has been thus programmed) to arrive at the expectation that something will happen from the facts of experience, however mistaken that expectation might turn out to be.

And here I shall now also provide an answer to Hume's other problem 'There is required a medium, which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument. What that medium is, I must confess, passes my comprehension; and it is incumbent on those to produce it, who assert that it really exists, and is the origin of all our conclusions concerning matter of fact.'

In brief, the answer is: Abduction - the mode of inference that consists in the proposing of hypotheses to account for (supposed) facts.

First, what is an inference? In logic, an inference is the assertion of a conclusion, in general because one has already asserted (and thus accepted) certain premisses one considers sufficient to assert the conclusion.

There are three basic kinds of inference, that cover very many specific sorts of inferences:

1. Deductions: To infer conclusions that follow from given assumptions.
2. Abductions: To infer assumptions from which given given conclusions follows.
Inductions: To confirm or infirm (support or undermine) assumptions by showing their conclusions do (not) conform to the observable facts.

Normally in reasoning all three kinds are involved: We explain supposed facts by abductions; we check the abduced assumptions by deductions of the facts they were to explain; and we test the assumptions arrived by deducing consequences and then revise by inductions the probabilities of the assumptions by probabilistic reasoning when these consequences are verified or falsified.

Next, here is a simple characterization of abduction by Charles S. Peirce, who first clearly identified this mode of inference and saw its importance:

"Abduction. (..) "Hypothesis [or abduction] may be defined as an argument which proceeds upon the assumption that a character which is known necessarily to involve a certain number of others, may be probably predicated of any object which has all the characteristics which this character is known to involve." (5.276) "An abduction is [thus] a method of forming a general prediction." (2.269) But this prediction is always in reference to an observed fact; indeed, an abductive conclusion "is only justified by its explaining an observed fact." (1.89) If we enter a room containing a number of bags of beans and a table upon which there is a handful of white beans, and if, after some searching, we open a bag which contains white beans only, we may infer as a probability, or fair guess, that the handful was taken from this bag. This sort of inference is called making an hypothesis or abduction. (J. Feibleman, "An Introduction to the Philosophy of Charles S. Peirce", p. 121-2. The numbers referred to are to paragraphs in Peirce's "Collected Papers".)

Accepting the conclusion that an explanation is needed when facts contrary to what we should expect emerge, it follows that the explanation must be such a proposition as would lead to the prediction of the observed facts, either as necessary consequences or at least as very probable under the circumstances. A hypothesis then, has to be adopted, which is likely in itself, and renders the facts likely. This step of adopting a hypothesis as being suggested by the facts, is what I call abduction. (Idem, p. 121-2)

Abduction (..) is the first step of scientific reasoning, as induction is the concluding step. Nothing has so much contributed to present chaotic or erroneous ideas of the logic of science as failure to distinguish the essentially different characters of different elements of scientific reasoning; and one of the worst of these confusions, as well as one of the commonest, consists in regarding abduction and induction together (often also mixed with deduction) as a simple argument.

Accordingly, it seems as if what is true of theories conforms to the following diagram, that involves 6 named arrows and three kinds of inference I will briefly comment on:

  • A Theory is a set of statements that accounts for some Observations.

  • An Observation is a statement of particular fact (usually known fact, sometimes presumptive fact).

  • A Theory is inferred by abduction from some Observations.

  • An abduction is an inference towards the best explanation for (presumed) facts. As a rule, abductions are creative hypotheses that may involve guesses and assumed postulated entities of many kinds.

  • The relation between an Observation and a theory is an explanation if the Observation can be deduced from the Theory.

  • A Prediction is a statement about some particular (usually a presumptive fact) that is deduced from a Theory.

  • An induction is a re-calculation of the probability of a theory, given that a Prediction of the theory is found to be true or false in fact. It is a deductive consequence based on probability theory.

  • A test is the deduction that a certain Observation is in fact implied or contradicted by a Prediction from  a Theory, and thus may serve for an inductive argument about the probability of the Theory.

  • An expectation is the deduction that an Observation is implied by a Prediction from a Theory.

It should be noted that all relations represented by arrows in the diagram other than abduction are deductions, but that what is here called induction also involves probability theory, next to standard logic, which is what is used for the other deductions indicated in the diagram.

What is here called induction is otherwise known as Bayesian reasoning, and consists in essence in recalculating the probability of a theory using probability theory and facts from experience.  

Next, what is here called abduction is normally a creative leap to account for some puzzling fact, and is based on imagination, fantasy, analogy or anything else that may be useful to account for something one has no ready-made convincing explanation for.

Abductions, in the form of the theories they produce, are tested and checked in two ways: First, by deducing the facts they are meant to explain from the theory that is supposed to explain them, and this is a necessary condition for the abduction to make sense. Second, by induction in the above sense, to infer what the probability of the theory should be given that one has made an observation that is implied or contradicted by a prediction that follows from the theory.

Note 25: This negative argument must certainly, in process of time, become altogether convincing, if many penetrating and able philosophers shall turn their enquiries this way and no one be ever able to discover any connecting proposit-ion or intermediate step, which supports the understanding in this conclusion. But as the question is yet new, every reader may not trust so far to his own penetration, as to conclude, because an argument escapes his enquiry, that therefore it does not really exist. For this reason it may be requisite to venture upon a more difficult task; and enumerating all the branches of human knowledge, endeavour to show that none of them can afford such an argument.

Here Hume pretends some modesty, with an ironical twist to it that he may have missed: When he claims that 'This negative argument must certainly, in process of time, become altogether convincing, if many penetrating and able philosophers shall turn their enquiries this way and no one be ever able to discover any connecting proposition or intermediate step' what he in fact says is that sufficiently many combinations of failures to explain the reasoning he wants explained will make it certain that the reasoning cannot be explained.

But since Hume knew that his argument was new and radical, he restates it once more, and I will chart it in the selections that follow.

Note 26: All reasonings may be divided into two kinds, namely, demonstrative reasoning, or that concerning relations of ideas, and moral reasoning, or that concerning matter of fact and existence. That there are no demonstrative arguments in the case seems evident; since it implies no contradiction that the course of nature may change, and that an object, seemingly like those which we have experienced, may be attended with different or contrary effects. May I not clearly and distinctly conceive that a body, falling from the clouds, and which, in all other respects, resembles snow, has yet the taste of salt or feeling of fire? Is there any more intelligible proposition than to affirm, that all the trees will flourish in December and January, and decay in May and June? Now whatever is intelligible, and can be distinctly conceived, implies no contradiction, and can never be proved false by any demonstrative argument or abstract reasoning ŕ priori.

In the opening statement of this quotation Hume harks back to an assumption he made in the beginning of the section, that I found fault with under Note 1, and he also restates the distinction, and adds an assumption, namely that the 'relations of ideas' all belong to 'demonstrative reasoning', by which he means the same as we do by deductive reasoning, which is always such that the premisses of a valid deductive argument cannot be true while the conclusion of the argument are not true.

Now if it is this sort of reasoning, that is deductively valid, that Hume desires in explanation of an non-deductive inference from contingent facts to contingent conclusions, then he surely is right that such deductive reasoning cannot be produced, precisely because the relation is supposed to be not known to be deductively valid to start with.

And the examples he gives indeed are all good examples of logical possibilities that do not square with ordinary expectations based on experience, but yet are logically possible for all that.

Note 27: If we be, therefore, engaged by arguments to put trust in past experience, and make it the standard of our future judgement, these arguments must be probable only, or such as regard matter of fact and real existence, according to the division above mentioned. But that there is no argument of this kind, must appear, if our explication of that species of reasoning be admitted as solid and satisfactory. We have said that all arguments concerning existence are founded on the relation of cause and effect; that our knowledge of that relation is derived entirely from experience; and that all our experimental conclusions proceed upon the supposition that the future will be conformable to the past. To endeavour, therefore, the proof of this last supposition by probable arguments, or arguments regarding existence, must be evidently going in a circle, and taking that for granted, which is the very point in question.

Here Hume attempts to answer the sort of probabilistic approach and attempted solution I mentioned above. His own argument presupposes his own definitions and assumptions, but may be recast without these and to the same effect: That so-and-so has happened with such-and-such a probability in the past, does not imply that so-and-so will happen with such-and-such a probability now or in the future.

This is true, but it is only a cogent argument if one disregards abduction, and tacitly insists that all cogent argumentation must be deductive, as Hume does. If one does not make these Humean assumptions, one can, with Newton, suppose that such theoretical assumptions as one has found to account deductively for the facts one desires to explain, and that are not refuted by such knowledge as one has, do hold irrespective of time, until refuted (or qualified) by further knowledge.

This makes such assumptions clearly guesses, that are only supported and not deductively proved by experiments, and that may be refuted by further experiments, but that is no valid objection to a scientific hypothesis.

There is a further difficulty Hume might raise here, that is in fact covered by the next quotation plus note:

Note 28: In reality, all arguments from experience are founded on the similarity which we discover among natural objects, and by which we are induced to expect effects similar to those which we have found to follow from such objects. And though none but a fool or madman will ever pretend to dispute the authority of experience, or to reject that great guide of human life, it may surely be allowed a philosopher to have so much curiosity at least as to examine the principle of human nature, which gives this mighty authority to experience, and makes us draw advantage from that similarity which nature has placed among different objects. From causes which appear similar we expect similar effects. This is the sum of all our experimental conclusions.

Hume's position is, in short, that, as a practical or as a scientific man he is quite willing to reason inductively and to expect that the future will be like the past, but that as philosopher he should like a reason for the assumption that 'From causes which appear similar we expect similar effects.'

Now here are two possible answers.

One proceeds from the assumption that all such reasons as are acceptable must be deductively valid, and follow deductively from known evidence. This is, in effect, Hume's position, and involves a tacit assumption that abductions do not exist or should be rejected because abductive inferences are not deductively valid.

The other proceeds from the assumption that one may give abductive reasons, and that the only standards abductions must satisfy is that they do deductively entail what they are supposed to explain and that there is no known evidence that refutes them.

And then one can simply assume that one lives in a reality in which there are both varying and constant properties and relations i.e. such properties and relations that do not remain the same in time and such as do, and that one can learn from experience at least some of these, and can learn this by guessing, experimentation, and probabilistic confirmation.

Note 29:  Now it seems evident that, if this conclusion were formed by reason, it would be as perfect at first, and upon one instance, as after ever so long a course of experience. But the case is far otherwise. Nothing so like as eggs; yet no one, on account of this appearing similarity, expects the same taste and relish in all of them. It is only after a long course of uniform experiments in any kind, that we attain a firm reliance and security with regard to a particular event.

Here Hume considers the sort of reasoning I proposed in Note 24, and insists in conclusion that 'It is only after a long course of uniform experiments in any kind, that we attain a firm reliance and security with regard to a particular event.'

Actually, this is not quite true: A burned child fears the fire, and not after having been burned many times, but after only one time.

Clearly, the reason is that a single painful experience is sufficient for the human mind to adopt fargoing hypotheses, such that all fire burns.

Note 30: Now where is that process of reasoning which, from one instance, draws a conclusion, so different from that which it infers from a hundred instances that are nowise different from that single one? This question I propose as much for the sake of information, as with an intention of raising difficulties. I cannot find, I cannot imagine any such reasoning. But I keep my mind still open to instruction, if any one will vouchsafe to bestow it on me.

I think I have given this reasoning, namely abduction, that accords with Newton's Rules of Reasoning in Philosophy, and was first clearly identified by Peirce.

Note 31: Should it be said that, from a number of uniform experiments, we infer a connexion between the sensible qualities and the secret powers; this, I must confess, seems the same difficulty, couched in different terms. The question still recurs, on what process of argument this inference is founded? Where is the medium, the interposing ideas, which join propositions so very wide of each other?

The answer is, in general terms: Probability theory.

Note 32: Here, then, is our natural state of ignorance with regard to the powers and influence of all objects. How is this remedied by experience? It only shows us a number of uniform effects, resulting from certain objects, and teaches us that those particular objects, at that particular time, were endowed with such powers and forces. When a new object, endowed with similar sensible qualities, is produced, we expect similar powers and forces, and look for a like effect. From a body of like colour and consistence with bread we expect like nourishment and support. But this surely is a step or progress of the mind, which wants to be explained. When a man says, I have found, in all past instances, such sensible qualities conjoined with such secret powers: And when he says, Similar sensible qualities will always be conjoined with similar secret powers, he is not guilty of a tautology, nor are these propositions in any respect the same. You say that the one proposition is an inference from the other. But you must confess that the inference is not intuitive; neither is it demonstrative: Of what nature is it, then? To say it is experimental, is begging the question. For all inferences from experience suppose, as their foundation, that the future will resemble the past, and that similar powers will be conjoined with similar sensible qualities. If there be any suspicion that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion. It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future; since all these arguments are founded on the supposition of that resemblance.

In this selection we have, I think, Hume's clearest general statement of his position concerning induction. Clearly, the basic problem is the inference that the future will be like the past in some respect. He says and asks:

When a man says, I have found, in all past instances, such sensible qualities conjoined with such secret powers: And when he says, Similar sensible qualities will always be conjoined with similar secret powers, he is not guilty of a tautology, nor are these propositions in any respect the same. You say that the one proposition is an inference from the other. But you must confess that the inference is not intuitive; neither is it demonstrative: Of what nature is it, then?

My answer is: Its nature is abductive. And indeed the inference from (1) 'I have found, in all past instances, such sensible qualities conjoined with such secret powers' to (2) 'Similar sensible qualities will always be conjoined with similar secret powers' is not deductively valid - but the inference of (1) from (2) is deductively valid, at least if 'always' is taken to extend also to the past, which shows that (2) can explain (1).

And the point that Hume did not clearly see - and that indeed Peirce may have been the first to see clearly - is that one need not invalidly infer (2) from (1) but that, since one must make assumptions anyway, one may assume (2) by abduction and infer (1) from it by deduction, and then seek to support (2) by deriving further consequences from it and comparing these with experience.

Here three remarks must be added concerning truth and probability.

First, when Hume speaks of the inference of (2) from (1) and rejects it, he speaks of deductive inference, and rightly rejects the proposed inference, because (2) may be false while (1) is true.

Second, when I speak of the abductive inference of (2) based on (1), I do not suggest that it is deductively valid, but I do suggest that the inference of (1) from (2) is deductively valid, and that this fact offers a ground to make (2) an assumption and is what makes the inference of (2) from (1) an abductive inference.

Third, the abductive inference of (2) does not make (2) true, but it does make it into a possibly true explanation of (1) that may be supported, undermined or refuted by further experimental evidence.

When Hume in the above quotation continues

To say it is experimental, is begging the question. For all inferences from experience suppose, as their foundation, that the future will resemble the past, and that similar powers will be conjoined with similar sensible qualities.

he is confused for several reasons.

First, the inference of (2) is by an abductive step, that was not obvious to Hume, and that he might have rejected as not deductively valid had he seen it, but this does not mean it is without experimental evidence. Indeed, the experimental evidence for it is summarized by (1).

Second, it is not true that 'all inferences from experience suppose, as their foundation, that the future will resemble the past', for experience also shows that some properties do not last forever, or occur only for a brief time. You may bend a steel wire many times, but eventually your continueing to bend it will break it; and many persons have for thousands of days expected that they would survive the next day, and yet died the next day.

Third, if Hume were to say here, as he probably would, that the eventual breaking of a steel wire by bending and the eventual dying of a man are both also learned from experience, I of course agree. My difference with Hume is that I hold that one can and does and may make abductive inferences based on experimental evidence, which result in hypothetical assumptions that deductively imply the evidence, and which one can then proceed to test by further experimental evidence, and which one may adopt as the best explanation until refuted or made improbable by experimental evidence.

Indeed, here is the place to remark that Newton's fourth Rule of Reasoning, where he says 'In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may be either made more accurate, or liable to exception' demands too much, and might be better restated along these lines: 'In experimental philosophy we are to look upon propositions inferred by abduction from phenomena as possible explanations, that may be true, and that can be tested when other relevant phenomena occur, by which they may be either made more accurate, or liable to exception.' 

In this context it is quite interesting that Hume also says

If there be any suspicion that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion.

Thus, Hume insists that we can learn from experience. His problem is that he presumes all steps of inference must be deductive, for which reason he cannot believe in the above inference of (2) from (1), and for which reason he concludes

It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future; since all these arguments are founded on the supposition of that resemblance.

This is true if one reads 'prove' as 'deductively prove', but not if one replaces it by 'suggest the abductive guess that, in specific cases there is'.

Hence it seems, in summary, that Hume's difficulties with induction are mainly due to the following two points:

A. He insists that all argumentation to be credible must be deductively valid.
B. He was not aware that assumptions may be supported by their verified consequences.

And the solution I offer (in line with Newton and Peirce) is accordingly based on

A'. Since we must make assumptions anyway, we may do so by abductions: To infer that a certain hypothesis makes sense, because it explains certain facts one cannot otherwise explain, while the hypothesis itself is not contradicted by such evidence as one has.
B'. One can support hypotheses and assumptions by their consequences with the help of probability theory: If T implies P and neither T nor P are certainly true or certainly false, then the probability of T given that P is verified is higher than it was before knowing P is verified, and is higher in proportion with P's improbability.

Here is the mathematics involved in the last point. Given that:

pr(P|T)=1 - T implies P so the probability of P given T is 1
pr(T)=t    -  Let t be the probability of T and assume 0<t<1
p(P)=p     -  Let p be the probability of P and assume 0<p<1

it follows that

pr(T|P)=pr(P|T)*p(T):pr(P) - by probability theory
          = t:p                     - by the above assumptions
t:p > t                             - since 0<p<1

In fairness to Hume it should be remarked that this mode of reasoning was hardly known in his day and age, though the Reverend Bayes did first articulate it in the 18th C as a way to learn from experience by probability theory.

Note 33: Let the course of things be allowed hitherto ever so regular; that alone, without some new argument or inference, proves not that, for the future, it will continue so. In vain do you pretend to have learned the nature of bodies from your past experience. Their secret nature, and consequently all their effects and influence, may change, without any change in their sensible qualities. This happens sometimes, and with regard to some objects: Why may it not happen always, and with regard to all objects? What logic, what process of argument secures you against this supposition? My practice, you say, refutes my doubts. But you mistake the purport of my question. As an agent, I am quite satisfied in the point; but as a philosopher, who has some share of curiosity, I will not say scepticism, I want to learn the foundation of this inference. No reading, no enquiry has yet been able to remove my difficulty, or give me satisfaction in a matter of such importance. Can I do better than propose the difficulty to the public, even though, perhaps, I have small hopes of obtaining a solution? We shall at least, by this means, be sensible of our ignorance, if we do not augment our knowledge.

Here it should be remarked that this whole Humean argument against reasoning in terms of Cause and Effect seemed to have been part of Hume's argument in favour of scepticism: "Look, there is not even a cogent deductive argument from Cause to Effect, though this mode of reasoning is the foundation of all experimental reasoning".

My answer to this is: You are right, but there is a cogent abductive argument of possible causes from effects, and such possible causes may then be tested further experimentally, and supported or infirmed probabilistically.

Note 34: It is certain that the most ignorant and stupid peasants—nay infants, nay even brute beasts—improve by experience, and learn the qualities of natural objects, by observing the effects which result from them. When a child has felt the sensation of pain from touching the flame of a candle, he will be careful not to put his hand near any candle; but will expect a similar effect from a cause which is similar in its sensible qualities and appearance. If you assert, therefore, that the understanding of the child is led into this conclusion by any process of argument or ratiocination, I may justly require you to produce that argument; nor have you any pretence to refuse so equitable a demand. You cannot say that the argument is abstruse, and may possibly escape your enquiry; since you confess that it is obvious to the capacity of a mere infant. If you hesitate, therefore, a moment, or if, after reflection, you produce any intricate or profound argument, you, in a manner, give up the question, and confess that it is not reasoning which engages us to suppose the past resembling the future, and to expect similar effects from causes which are, to appearance, similar. This is the proposition which I intended to enforce in the present section. If I be right, I pretend not to have made any mighty discovery. And if I be wrong, I must acknowledge myself to be indeed a very backward scholar; since I cannot now discover an argument which, it seems, was perfectly familiar to me long before I was out of my cradle.

As I pointed out above, the case of the burned child that fears the fire contradicts Hume earlier statement that 'It is only after a long course of uniform experiments in any kind, that we attain a firm reliance and security with regard to a particular event', though it may be granted that the 'security' that the burned child feels about the dangers of fire is psychological and mostly due to the pain felt rather than the number of instances.

Now what Hume want to establish in his section IV, that is indeed intentionally titled Sceptical doubts concerning the operations of the understanding, is that 'it is not reasoning which engages us to suppose the past resembling the future, and to expect similar effects from causes which are, to appearance, similar'.

It seems to me that Hume failed, and that Peirce was the first to clearly see why and how: By not admitting the possibility of abductive inference; by not being aware of the mathematical fact that one can confirm guesses probabilistically; and by not paying more attention to the fact that all human reasoning proceeds by assumptions, which one is free to make, and can support by their consequences.

And it also should be said, in fairness to Newton, that it is likely, given his Rules of Reasoning, that Newton was at least aware of the possibility of abductive inference, for his rules support, suppose and circumscribe it, and indeed his whole Principia illustrates it.

Finally, there is a considerably longer and somewhat more technical essay on the Problem of Induction on this site, that I wrote 1980-1983. This also treats Goodman's so called New Riddle of Induction, that is indeed a sharpening of Hume's points. Some of this essay was used above. And there is a briefer treatment of induction in my Philosophical Dictionary.

The above are my notes to David Hume's Section IV of his Enquiry concerning Human Understanding. There is considerably more on the subject on my site, but the essay about it that I also wrote originally in the 1980ies - see the link for its start - still needs some final editing. Even so, part 1 is a better logical analysis of the problem than I have read elsewhere.

P.S. Corrections, if any are necessary, have to be made later.

(Note on the formatting of Nederlog: See the last underlined link, and please note that even if it doesn't look as it should in an MS IE webbrowser, it does look as intended in Firefox and in Seamonkey, and indeed was written mostly in the Composer of the last fine Mozilla-browser. The necessary repairs are in the works, as the saying is - and the text is readable anyway, even in rotten browsers.)

And the reason there was no Nederlog since June 3 is that I again am caught in a vicious circle of too much pain and too little sleep. If therefore there is nothing the following days, that is the most probable explanation.

Also, it is likely there will be less about ME in Nederlog - there being so very many scientifically highly capable patients with ME on forums for people with ME, all at least as gifted as I am - and more about philosophy, logic, politics, literature or science, because I found that in fact I really completely lack the moral and intellectual gifts of Bob and Gerwyn and Patricia Carter and co. and have no hope in hell to acquire such great gifts either, ever, prefrontal lobotomy apart.


                              As to ME/CFS (that I prefer to call ME):

1.  Anthony Komarof Ten discoveries about the biology of CFS (pdf)
3.  Hillary Johnson The Why
4.  Consensus of M.D.s Canadian Consensus Government Report on ME (pdf)
5.   Eleanor Stein Clinical Guidelines for Psychiatrists (pdf)
6.  William Clifford The Ethics of Belief
7.  Paul Lutus

Is Psychology a Science?

8.  Malcolm Hooper Magical Medicine (pdf)
 Maarten Maartensz
ME in Amsterdam - surviving in Amsterdam with ME (Dutch)
 Maarten Maartensz Myalgic Encephalomyelitis

Short descriptions of the above:                

1. Ten reasons why ME/CFS is a real disease by a professor of medicine of Harvard.
2. Long essay by a professor emeritus of medical chemistry about maltreatment of ME.
3. Explanation of what's happening around ME by an investigative journalist.
4. Report to Canadian Government on ME, by many medical experts.
5. Advice to psychiatrist by a psychiatrist who understands ME is an organic disease
6. English mathematical genius on one's responsibilities in the matter of one's beliefs:
7. A space- and computer-scientist takes a look at psychology.
8. Malcolm Hooper puts things together status 2010.
9. I tell my story of surviving (so far) in Amsterdam with ME.
10. The directory on my site about ME.

See also: ME -Documentation and ME - Resources
The last has many files, all on my site to keep them accessible.

Maarten Maartensz (M.A. psy, B.A. phi)
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